BANK & INSURANCE (QUADRATIC EQUATION PART 1)

Total Questions: 50

21. I. x² + 10x - 56 = 0

II. y² - 17y + 60 = 0

Correct Answer: (a) x < y
Solution:

From I:
x² + 10x - 56 = 0
x² + 14x - 4x - 56 = 0
x(x + 14) - 4(x + 14) = 0
(x + 14)(x - 4) = 0
x = -14, 4

From II:
y² - 17y + 60 = 0
y² - 12y - 5y + 60 = 0
y(y - 12) - 5(y - 12) = 0
(y - 12)(y - 5) = 0
y = 12, 5

22. I. x² - 13x - 68 = 0

II. y² - 3y - 54 = 0

Correct Answer: (c) x = y or No relation
Solution:

From I:
x² - 13x - 68 = 0
x² - 17x + 4x - 68 = 0
x(x - 17) + 4(x - 17) = 0
(x - 17)(x + 4) = 0
x = 17, -4

From II:
y² - 3y - 54 = 0
y² - 9y + 6y - 54 = 0
y(y - 9) + 6(y - 9) = 0
(y - 9)(y + 6) = 0
y = 9, -6

23. I. x = √144 

II. y³ = 729

Correct Answer: (d) x > y
Solution:

From I:
x = √144
x = 12

From II:
y³ = 729
y = 9

24. I. x² - 18x + 77 = 0   

II. y² - 18y + 45 = 0

Correct Answer: (c) x = y or No relation
Solution:

From I:
x² - 18x + 77 = 0
x² - 11x - 7x + 77 = 0
x(x - 11) - 7(x - 11) = 0
(x - 11)(x - 7) = 0
x = 11, 7

From II:
y² - 18y + 45 = 0
y² - 15y - 3y + 45 = 0
y(y - 15) - 3(y - 15) = 0
(y - 15)(y - 3) = 0
y = 15, 3

25. I. x² - 17x + 72 = 0   

II. y² - 12y + 32 = 0

Correct Answer: (e) x ≥ y
Solution:

From I:
x² - 17x + 72 = 0
x² - 8x - 9x + 72 = 0
x(x - 8) - 9(x - 8) = 0
(x - 8)(x - 9) = 0
x = 8, 9

From II:
y² - 12y + 32 = 0
y² - 8y - 4y + 32 = 0
y(y - 8) - 4(y - 8) = 0
(y - 8)(y - 4) = 0
y = 8, 4

26. I. 2x² - 39x + 180 = 0  

II. 2y² - 7y - 30 = 0

Correct Answer: (d) x > y
Solution:

2x² - 39x + 180 = 0
2x² - 24x - 15x + 180 = 0
2x(x - 12) - 15(x - 12) = 0
(x - 12)(2x - 15) = 0
x = 12, 15/2

2y² - 7y - 30 = 0
2y² - 12y + 5y - 30 = 0
2y(y - 6) + 5(y - 6) = 0
(y - 6)(2y + 5) = 0
y = 6, -5/2

27. 27. I. 4x² - 21x - 18 = 0  

II. 4y² + 19y + 12 = 0

Correct Answer: (e) x ≥ y
Solution:

4x² - 21x - 18 = 0
4x² - 24x + 3x - 18 = 0
4x(x - 6) + 3(x - 6) = 0
(x - 6)(4x + 3) = 0
x = 6, -3/4

4y² + 19y + 12 = 0
4y² + 16y + 3y + 12 = 0
4y(y + 4) + 3(y + 4) = 0
(y + 4)(4y + 3) = 0
y = -4, -3/4

28. I. 5x² - 48x + 64 = 0  

II. 3y² - 56y + 256 = 0

Correct Answer: (b) x ≤ y
Solution:

28. (b): 5x² - 48x + 64 = 0
5x² - 40x - 8x + 64 = 0
5x(x - 8) - 8(x - 8) = 0
(x - 8)(5x - 8) = 0
x = 8, 8/5

3y² - 56y + 256 = 0
3y² - 24y - 32y + 256 = 0
3y(y - 8) - 32(y - 8) = 0
(y - 8)(3y - 32) = 0
y = 8, 32/3

29. I. x² = 49         

II. 3y² - 47y + 182 = 0

Correct Answer: (b) x ≤ y
Solution:

x² = 49
x = 7, -7

3y² - 47y + 182 = 0
3y² - 21y - 26y + 182 = 0
3y(y - 7) - 26(y - 7) = 0
(y - 7)(3y - 26) = 0
y = 7, 26/3

30. I. x² - 17x + 72 = 0  

II. 2y² - 39y + 189 = 0

Correct Answer: (b) x ≤ y
Solution:

x² - 17x + 72 = 0
x² - 9x - 8x + 72 = 0
x(x - 9) - 8(x - 9) = 0
(x - 9)(x - 8) = 0

x = 9, 8

2y² - 39y + 189 = 0
2y² - 18y - 21y + 189 = 0
2y(y - 9) - 21(y - 9) = 0
(y - 9)(2y - 21) = 0
y = 9, 21/2